Multiple stacked planes image distortion (Noisey Images effect)
A way to achieve a similar effect is the following:


Use several planes or parts of planes
One on background with the full image
Others with marks or dust and an alpha transparency
Others which cover only a part of the original image and moving between the background and the camera


low quality gif here...


The animation is the following. Planes are simply moving and/or scaling in face of the camera. 



Two materials are used:


A simple texture on one plane





A texture with transparency for others




The plane UV are adapted to cut parts of the images where needed (you can adapt depending on what you want):